An electrostatic dust precipitator that is installed in a factory smokestack includes a straight metal wire of length 0.7 m that
is charged approximately uniformly with a total charge 0.8 ×10−7 C. A speck of coal dust (which is mostly carbon) is near the wire, far from both ends of the wire; the distance from the wire to the speck is 1.4 cm. Carbon has an atomic mass of 12 (6 protons and 6 neutrons in the nucleus). A careful measurement of the polarizability of a carbon atom gives the value 1.96 × 10−40 (C · m)/(N/C). (a) Calculate the initial acceleration of the speck of coal dust, neglecting gravity. Your answer must be expressed in terms of , and . You can use other quantities in your calculations, but your final result must not include them. It is convenient to use the "binomial expansion" that you may have learned in calculus, that if . Note that can be negative. (Enter the magnitude. Use the following as necessary: , , , and for the mass of a carbon atom. Use the binomial expansion in your answer.)
1 answer:
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Answer:
1.) answer B
2.) answer D
3.) answer A
Explanation:
In all of these problems, it is essential to draw pictures in order to understand which trigonometric function to use according to the angle that the vector in question forms with the component requested. For all of them try to picture a right angle triangle with the vector as the hypotenuse, and the components as the triangle's shorter sides. Please refer to the three pictures attached as image for this answer a,d notice that the vector quantity known for all cases is represented in red, and the component to find is represented in green.
Problem 1) : the vector velocity makes an angle of 24 degrees with the edge of the table. So picture that vector as the hypotenuse of a right angle triangle for which you know the value: 1.8 m/s
So in this case, where you know the angle, the hypotenuse, and need to find the adjacent side to the angle, you use the cosine function as follows:
requested component
which we round to 1.6 to match answer C).
For problem 2.) wee need to find the component opposite to the given angle in the triangle for which we also know the hypotenuse. So we use the sine function as follows:
requested component
which we round to 135.9 m to match answer D).
For problem 3.) we need to find the horizontal component to the acceleration which corresponds to the adjacent side to the known angle, so we use the cosine function as follows:
requested component
which we round tp 7.7 to match answer A).
